研究显示，即使未显式协作，简单定价算法也能推动高价形成。2019年实验表明，两套互相学习的算法会通过“试错+报复性降价”形成类默契合谋，从而维持高价。2024年研究指出，当两个无交换后悔（no-swap-regret）算法对决时，将自然收敛到竞争性价格，无法形成合谋；但在2025年最新结果中，一种看似无害的“非响应式策略”（固定概率随机定价）在与无交换后悔算法对决时会诱导后者提高价格，并通过偶尔压价获利。这导致高价均衡，且双方利润接近、无改变策略动机，使买方长期处于不利状态。

关键量化结构在于这种非响应式策略会对极高价格赋予显著概率权重，同时为大量较低价格分配较小概率，从而最大化对手算法的学习偏差。研究团队发现，多种不同概率组合都能导致高价均衡，使监管更难识别问题，因为无交换后悔算法本身在对阵同类算法时可保证竞争性价格，却在面对另一类算法时表现失灵。监管者无法依赖传统“威胁行为”或“合谋意图”标准，因为算法既无沟通也无响应逻辑，但结果等同于合谋。

政策含义极具挑战性。若要求所有卖方使用无交换后悔算法，可确保在算法之间的竞争中价格下降，但该方法无法防止人类卖家或简单策略参与者操纵价格结构。算法身份验证机制虽可检测某算法是否具备无交换后悔性质，但无法阻止非响应式定价的“单边高价”效应。整体趋势表明，算法定价的博弈论结构比传统反垄断假设更复杂，且高价可在无威胁、无沟通、无意图情况下自发出现。

Research shows that even without explicit coordination, simple pricing algorithms can drive prices upward. A 2019 experiment demonstrated that two learning algorithms can develop tacit collusion via “trial-and-error plus retaliatory undercutting,” sustaining high prices. A 2024 result showed that two no-swap-regret algorithms converge to competitive prices, but 2025 findings reveal that a seemingly benign “nonresponsive strategy” (fixed-probability random pricing) induces a no-swap-regret opponent to raise prices, while the nonresponsive player profits by occasionally undercutting. This produces a high-price equilibrium with near-equal profits and no incentive for either side to switch strategies, leaving buyers persistently disadvantaged.

The quantitative structure hinges on the nonresponsive strategy assigning substantial probability mass to very high prices, with smaller probabilities spread across many lower prices, maximizing distortion of the opponent’s learning process. Researchers found that many different probability assignments generate similar high-price equilibria, complicating regulation. No-swap-regret algorithms yield competitive outcomes only against each other; when facing different algorithms, they fail to prevent inflated prices. Regulators cannot rely on traditional markers such as “threats” or “intent,” because the algorithms communicate nothing yet produce collusion-like outcomes.

Policy implications are severe. Enforcing universal use of no-swap-regret algorithms would lower prices in algorithm-only markets but cannot prevent human sellers or simple strategies from manipulating price dynamics. Verification tools can test whether an algorithm satisfies no-swap-regret properties but cannot block unilateral high-price effects of nonresponsive strategies. Overall, game-theoretic dynamics in algorithmic pricing are more complex than classical antitrust assumptions, and high prices can arise spontaneously without threats, communication, or intent.